From quantum field theory to quantum mechanics

Nuovo cimento della Societa italiana di fisica. B, Relativity, classical and statistical physics, 2005

A realistic physical axiomatic approach of the relativistic quantum field theory is presented. Following the action principle of Schwinger, a covariant and general formulation is obtained. The correspondence principle is not invoked and the commutation relations are not postulated but deduced. The most important theorems such as spin-statistics, and CPT are proved. The theory is constructed form the notion of basic field and system of basic fields. In comparison with others formulations, in our realistic approach fields are regarded as real things with symmetry properties. Finally, the general structure is contrasted with other formulations.

The Routledge Companion to Philosophy of Physics, 2022

The consensus view among philosophers of physics is that relativistic quantum field theory (QFT) does not describe particles. That is, according to QFT, particles are not fundamental entities. How is this negative conclusion compatible with the positive role that the particle notion plays in particle physics? The first part of this chapter lays out multiple lines of negative argument that all conclude that QFT cannot be given a particle interpretation. These arguments probe the properties of the ‘particles’ in standard formulations of QFT and the limited applicability of ‘particle’ representations. The second part of the chapter surveys proposals for nonfundamental roles that the particle concept plays in particle physics. The conclusion suggests directions for future philosophical research.

2011

An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schrödinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discreteness of particles is traced back to the discreteness of occupation numbers or Ising-spins, while the continuity of the wave function reflects the continuity of the probability distribution for the Ising-spins.

Physics of Particles and Nuclei, 2015

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable effect in standard theory is the wave packet spreading (WPS) of the photon coordinate wave function in directions perpendicular to the photon momentum. This leads to several paradoxes. The most striking of them is that coordinate wave functions of photons emitted by stars have cosmic sizes and strong arguments indicate that this contradicts observational data. We argue that the above postulate is based neither on strong theoretical arguments nor on experimental data and propose a new consistent definition of the position operator. Then WPS in directions perpendicular to the particle momentum is absent and the paradoxes are resolved. Different components of the new position operator do not commute with each other and, as a consequence, there is no wave function in coordinate representation. Implications of the results for entanglement, quantum locality and the problem of time in quantum theory are discussed.

Lecture Notes in Physics, 2007

We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum gravity and string theory.

Progress of Theoretical Physics, 1982

arXiv (Cornell University), 2021

The wave-particle duality, while being supported by overwhelming scientific evidence, is now claimed outdated by some physics professionals. They declare that the Quantum Field Theory allows only field aspect of reality. Presented below are the arguments showing that the Quantum Field Theory embraces the whole range of the Field-Particle Duality with both its extremes. We also discuss the important new experiments which reinforce the particle side of the story and thereby confirm the Field-Particle Duality.

1995

Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second quantization to the path-integral technique in Euclidean space, where there is an immediate connection with the rules for Feynman diagrams and the partition function of Statistical Mechanics.

Entropy

The elementary particles of relativistic quantum field theory are not simple field quanta, as has long been assumed. Rather, they supplement quantum fields, on which they depend on but to which they are not reducible, as shown here with particles defined instead as a unified collection of properties that appear in both physical symmetry group representations and field propagators. This notion of particle provides consistency between the practice of particle physics and its basis in quantum field theory.